Nuclear fuel failure protection method

ABSTRACT

A method that provides a more direct indication of peak fuel rod centerline temperature and peak fuel rod clad temperature than conventionally inferred from the power distribution by directly and continuously measuring the fuel temperatures of the fuel pellets in one or more of the hottest fuel elements in the core. The peak fuel rod clad temperature is then obtained from the maximum measured peak fuel rod centerline temperature in combination with the maximum coolant core exit temperature and the minimum coolant flow rate.

CROSS-REFERENCE TO RELATED APPLICATION

This application claims priority from and claims the benefit of U.S.Provisional Application Ser. No. 62/625,393, filed Feb. 2, 2018, andentitled “NUCLEAR FUEL FAILURE PROTECTION METHOD.”

BACKGROUND 1. Field

This invention pertains generally to a method of determining reactorcore operating parameters and, more particularly, to a method of moreaccurately monitoring the peak fuel rod centerline temperature anddetermining the fuel rod peak clad temperature and the closeness tocritical operating limits for those parameters.

2. Related Art

In many state-of-the-art nuclear reactor systems in-core sensors areemployed for directly measuring the radioactivity within the core at anumber of axial elevations. Thermocouple sensors are also located atvarious points around the core at an elevation where the coolant exitsthe core to provide a direct measure of coolant outlet temperature atvarious radial locations. These sensors are used to directly measure theradial and axial distribution of power inside the reactor core. Thispower distribution measurement information is used to determine whetherthe reactor is operating within nuclear power distribution limits. Thetypical in-core sensor used to perform this function is a self-powereddetector that produces an electric current that is proportional to theamount of fission occurring around it. This type of sensor is generallydisposed within an instrument thimble within various fuel assembliesaround the core, does not require an outside source of electrical powerto produce the current, is commonly referred to as a self-powereddetector and is more fully described in U.S. Pat. No. 5,745,538, whichis incorporated in its entirety herein by reference.

Another type of sensor capable of measuring various parameters of thecore, which is typically disposed within the instrument thimbles invarious fuel assemblies around the core is described in U.S. PatentApplication Publication No. 2018/0218797, which is incorporated in itsentirety herein by reference. This type of sensor employs a transmitterdevice that includes a self-powered neutron detector structured todetect neutron flux, a capacitor electrically connected in parallel withthe neutron detector, a gas discharge tube having an input end and anoutput end, and an antenna electrically connected to the output end inseries with a resonant circuit. The input end of the gas discharge tubeis electrically connected to the capacitor. The antenna is structured toemit a signal comprising a series of pulses representative of theintensity of the neutron flux monitored by the self-powered detector.Other core parameters can also be monitored by their effects on alteringthe values of the inductance and capacitance of the resonant circuit.

Still another in-core sensor that does not require signal leads tocommunicate its output out of the reactor is disclosed in U.S. Pat. No.4,943,683, which is incorporated in its entirety herein by reference,which describes an anomaly diagnosis system for a nuclear reactor corehaving an anomaly detecting unit incorporated into a fuel assembly ofthe nuclear reactor core, and a transmitter-receiver provided outsidethe reactor vessel. The transmitter-receiver transmits a signalwirelessly to the anomaly detecting unit and receives an echo signalgenerated by the anomaly detecting unit wirelessly. When the anomalydetecting unit detects an anomaly in the nuclear reactor core, such asan anomalous temperature rise in the fuel assembly, the mode of the echosignal deviates from a reference signal. Then the transmitter-receiverdetects the deviation of the echo signal from the reference signal andgives an anomaly detection signal to a plant protection system. Thesensor actually monitors coolant temperature around the fuel assembly inwhich it is mounted.

Each of the foregoing sensors directly monitor conditions within thecore of a nuclear reactor, but none of the sensors directly monitorconditions within a nuclear fuel rod in the core during reactoroperation. Before advanced fuel cladding materials can be put intocommercial use they have to be rigorously tested to receive regulatoryapproval. The existing methodology for testing advanced fuel claddingmaterials requires fuel rods to be tested over several fuel cycles andexamined at the end of the irradiation test. This is a lengthy processthat takes several years during which time fuel cladding data is notavailable. In the existing method, critical data is only obtained duringthe post irradiation examination activities. What is desired is anin-pile sensor that can be placed within a fuel rod, endure thehazardous conditions over several fuel cycles and does not require fuelrod penetrations.

Furthermore, the critical reactor core operating parameters that have tobe monitored to ensure that the applicable nuclear fuel rod failurelimits are not reached, to assure safe reactor operation, are themaximum measured internal fuel rod temperature (T_(M)) and the peak cladtemperature (Tc). In current reactor protection system designs, thesevalues are inferred from fuel fission rate distribution inferences drawnfrom the above-noted neutron detectors and bulk indications of reactorvessel coolant temperature and coolant flow rate. The lack of detailedfuel rod internal temperature information imposes the need forconservative assumptions on the relationships between the nuclearradiation distribution, reactor vessel temperature distribution, and thecorresponding peak T_(M) and Tc values in the reactor. The assumedconservatisms increase the cost of the electricity produced by thereactor. An in-pile sensor that can be placed within a fuel rod wouldalso minimize the need for such conservatism.

SUMMARY

The disclosed concept achieves the foregoing objectives by providing amethod of determining a maximum measured internal fuel rod temperatureand a peak clad temperature of one or more of fuel rods in an operatingnuclear core comprising the steps of: directly measuring thetemperatures at one or more locations within the one or more of the fuelrods; identifying a hottest temperature within the one or more fuel rodsas the maximum measured internal fuel rod temperature and a corelocation where the hottest temperature is measured; measuring themaximum temperature of coolant exiting the core at the core locationwhere the hottest temperature is measured and the minimum flow rate ofthe coolant; and determining the peak clad temperature from the maximummeasured internal fuel rod temperature, the maximum temperature of thecoolant exiting the core at the core location where the hottesttemperature is measured and the minimum flow rate of the coolant.

In one embodiment the directly measuring step measures the temperaturealong a plurality of axial locations in the one or more fuel rods. Theplurality of axial locations may include the top and bottom of the fuelrods.

In one embodiment, determining the peak clad temperature is based onknowledge of heat transfer and geometric characteristics of fuel pelletsin the one or more fuel rods and cladding of the one or more fuel rod.The step of directly measuring the temperature at one or more locationson the fuel may be performed substantially continuously.

BRIEF DESCRIPTION OF THE DRAWINGS

A further understanding of the invention can be gained from thefollowing description of the preferred embodiments when read inconjunction with the accompanying drawings in which:

FIG. 1 is a schematic system diagram of a sensor system in accordancewith an example embodiment of the disclosed concept;

FIG. 2 is a circuit diagram of a sensor system in accordance with anexample embodiment of the disclosed concept;

FIG. 3 is a schematic diagram of a sensor using a liquid metalthermometer in accordance with an example embodiment of the disclosedconcept;

FIG. 4 is a flowchart of a method of determining a maximum measuredinternal fuel rod temperature and a peak clad temperature of one or moreof fuel rods in an operating nuclear core in accordance with an exampleembodiment of the disclosed concept.

DESCRIPTION OF THE PREFERRED EMBODIMENT

FIG. 1 is a schematic diagram of a sensor system in accordance with anexample embodiment of the disclosed concept. The system includes asensor 20 disposed in a fuel rod 10 of a nuclear reactor. The sensor 20includes a transmitting and/or receiving element 22 and a sensingelement 24. However, it will be appreciated that the transmitting and/orreceiving element 22 may be combined into a single circuit such as isshown and described with respect to FIG. 2. The sensing element 24 isstructured to sense one or more characteristics within the fuel rod suchas, without limitation, pellet temperature 12, pellet elongation 14, androd pressure 16. For example, electrical properties of the sensingelement 24 are affected based on changes in one or more characteristicswithin the fuel rod 10. The transmitting and/or receiving element 22 isstructured to transmit the sensed information. In some exampleembodiments, the transmitting and/or receiving element 22 is structuredto oscillate at different frequencies based on the sensedcharacteristics.

The sensor system also includes an instrument thimble 30 including acorresponding transmitting and/or receiving element 32. In some exampleembodiments of the disclosed concept, the transmitting and/or receivingelement 32 in the instrument thimble 30 is structured to interrogate thetransmitting and/or receiving element 22 in the sensor 20. For example,the transmitting and/or receiving element 32 in the instrument thimble30 may interrogate the transmitting and/or receiving element 32 in thesensor 20 by outputting a radio frequency signal and sensing the outputof the transmitting and/or receiving element 22 in the sensor 20,similar to the operation of a radio frequency identification (RFID)system. The output of the sensor 20, such as its oscillation frequency,may be indicative of characteristics within the fuel rod 10 such aspellet temperature 12. For example, center-line fuel temperature can becorrelated to the inductance change in a resonant circuit of the sensor20 resulting from a temperature change within the fuel rod 10 and,therefore, the resonant frequency change resulting from the change ininductance, can be detected at the instrument thimble 30.

The sensor system may also include another transmitting and/or receivingelement 42 and signal processing elements 44 located in a mildenvironment 40, such as outside the nuclear reactor core. The equipmentlocated in the mild environment may be structured to receive outputs ofthe instrument thimble 30, and may be used to process the output of theinstrument thimble 30. For example, the signal processing elements 44,may include a processor and/or memory structured to determinetemperature characteristics, such as the maximum measured internal fuelrod temperature (T_(M)), based on the output of the instrument thimble30. The signal processing elements 44 may use T_(M) to calculate thelimiting Peak Clad Temperature (Tc). A Reactor Protection System (RPS)may then use the values of T_(M) and Tc to determine whether a reactortrip should occur to ensure the required health and safety of thegeneral public is maintained under all operating conditions.

It will be appreciated that any suitable type of sensor may be employedas sensor 20. Some example embodiments of sensors are described hereinin connection with FIGS. 2 and 3. However, it will be appreciated thatother types of sensors may be employed without departing from the scopeof the disclosed concept. In some example embodiments of the disclosedconcept, the sensor 20 is passive. However, it will be appreciated thatand active sensor (i.e., one that requires a power source) may also beemployed without departing from the scope of the disclosed concept.

FIG. 2 is a circuit diagram of a sensor system in accordance with anexample embodiment of the disclosed concept. In the example embodimentof FIG. 2, the sensor 20 is formed by a resonant circuit. The sensor 20is structured such that the characteristics of the resonant circuitchange based on changes in characteristics within the fuel rod 10 suchas temperature. Thus, the output frequency of the sensor 20 will changebased on changes in temperature within the fuel rod 10. In some exampleembodiments, the resonant circuit may include a temperature sensitiveelectrical component, whose electrical characteristics change based ontemperature. For example, inductor L2 or capacitor C2 may be temperaturesensitive electrical components. In another example embodiment, atemperature sensitive resistor is added to form an RLC resonant circuit.In another example embodiment, a liquid thermometer is used, whichcauses inductor L2 to change inductance, which will be described inconnection with FIG. 3. The values of the components of the resonantcircuit can be chosen so that the return pulse has a unique frequencyfrom which the source of the return pulse can be identified, i.e., thefuel rod from which the return pulse emanated.

The example embodiment shown in FIG. 2 also includes a calibrator, whichis another resonant circuit formed by capacitor C1 and inductor L1. Thecalibrator does not include any temperature sensitive electriccomponents, so its output with remain constant regardless of changes intemperature. This allows the sensor system to calibrate and correct forcomponent degradation and drift. In addition to interrogating the sensorcircuit, the instrument thimble 30 will also interrogate the calibratorresonant circuit, which is static. The calibrator circuit response isused to correct any sensor signal change associated with componentdegradation or temperature drift.

As shown in FIG. 2, the instrument thimble 30 includes a transmittingand receiving component, formed by inductors L3 and L4. The transmittingcomponent may be used to interrogate the sensor 20 and the receivingcomponent may sense the response.

FIG. 3 is a schematic diagram of a sensor employing a liquid metalthermometer in accordance with an example embodiment of the disclosedconcept. The sensor includes an inductor coil 50, a ferritic core 52,and a liquid metal thermometer 54. The liquid metal thermometer 54 isplaced proximate to fuel pellets 56 in a fuel rod, such as the fuel rod10 of FIG. 1. The inductance of the inductor coil 50 is dependent on themagnetic permeability of the ferritic core 52 within the coil. If thisferritic core 52 is removed or inserted into the coil 50, the inductancewill change relative to its position. Using this methodology, centerline temperature within a fuel rod can be measured with the use of theliquid metal thermometer 54. For example, the liquid metal in the liquidmetal thermometer 54 with expand and contract with temperature changeswithin the fuel rod. The ferritic core 52 floats on top of the liquidmetal and, thus, the ferritic core 52 will move further into or out ofthe inductor coil 50 (causing changes in inductance) based on changes intemperature within the fuel rod.

The sensor shown in FIG. 3 may be employed as the sensors 20 shown inFIG. 1 or 2. For example, the inductor coil 50 and ferritic core 52 mayform inductor L2 shown in FIG. 2.

The acquired temperature data from the foregoing embodiment may bemeasured continuously. In principal, the temperature sensors used by thedevice described above could be placed at multiple axial positions inthe fuel rods in the fuel assemblies located in the reactor core. Thisincludes the top and bottom of the fuel rod and could include additionalaxial positions in the fuel rod. A number of these sensors distributedin the fuel rods expected to have the highest power level in the reactorcan be used to determine the most limiting fuel temperature. The fuelrods having the highest power level can be determined from a measure ofthe core power distribution which is routinely run. When the centerlinefuel temperature measurements are used in conjunction with the measuredcorresponding maximum coolant fluid temperature and minimum coolant flowrate obtained from existing sensors, the value of T_(M) can be used tocalculate the value of Tc. Any suitable existing sensor may be employedto measure the maximum coolant fluid temperature and minimum coolantflow rate. The RPS may then use the values of T_(M) and Tc to determinewhether a reactor trip should occur to ensure the required health andsafety of the general public is maintained under all operatingconditions.

M. M. El-Wakil, “Nuclear Heat Transport”, American Nuclear Society,copyright 1971, Third Printing, Section 5-6, which is incorporated inits entirety herein by reference, provides a description of how thevalue of Tc can be generated based on knowledge of T_(M), coupled withthe surrounding bulk coolant temperature (T_(F)) and knowledge of theheat transfer characteristics of the fuel pellet and fuel rod structuralmaterials. T_(F) is determined from the maximum coolant fluidtemperature and minimum coolant flow rate. An expression for Tc as afunction of time, derived from a corresponding measured T_(M) and T_(F),coupled with known heat transfer characteristics of the fuel pellets andfuel rod sheath is:

$\begin{matrix}{{T_{C}(t)} = {{T_{F}(t)} + \frac{{T_{M}(t)} - {T_{F}(t)}}{\phi (t)}}} & {{Eq}.\mspace{14mu} 1} \\{{Where}\text{:}} & \; \\{{\phi (t)} = \left( {{\frac{rh}{2{k_{f}\left( {T_{F}(t)} \right)}}\frac{A_{r + c}}{A_{r}}} + {\frac{ch}{k_{c}}\frac{A_{r + c}}{A_{m}}} + 1} \right)} & {{Eq}.\mspace{14mu} 2} \\{{And}\text{:}} & \; \\{{A_{m} = \frac{2\pi \; {cL}}{\ln \left\lbrack \frac{r + c}{r} \right\rbrack}}{{Where}\text{:}}{r = {{fuel}\mspace{14mu} {pellet}\mspace{14mu} {diameter}}}\text{}{c = {{cladding}\mspace{14mu} {thickness}}}\text{}{L = {{fuel}\mspace{14mu} {rod}\mspace{14mu} {length}}}\text{}{{kf} = {{fuel}\mspace{14mu} {pellet}\mspace{14mu} {thermal}\mspace{14mu} {conductivity}}}\text{}{{kc} = {{cladding}\mspace{14mu} {thermal}\mspace{14mu} {conductivity}}}{{Ar} = {{cross}\mspace{14mu} {section}\mspace{14mu} {area}\mspace{14mu} {of}\mspace{14mu} {fuel}\mspace{14mu} {pellet}}}\text{}{{{Ar} + c} = {{cross}\mspace{14mu} {sectional}\mspace{14mu} {area}\mspace{14mu} {of}\mspace{14mu} {fuel}\mspace{14mu} {pellet}\mspace{14mu} {and}}}\text{}{cladding}\text{}{h = {{cladding}\mspace{14mu} {heat}\mspace{14mu} {transfer}\mspace{14mu} {coefficient}\mspace{14mu} {by}\mspace{14mu} {{convection}.}}}} & {{Eq}.\mspace{14mu} 3}\end{matrix}$

An additional adjustment to the form of φ(t) to account for the thermalresistivity of a gap between the fuel pellet and cladding may be addedby those skilled in the art to account for expected changes in fuelcharacteristics.

The values of Tc will need to be increased to account for uncertaintiesassociated with the values of the constants, the measured values ofT_(F) and T_(M), and the expected difference between the limiting valueof Tc and the value of Tc determined at the position of the measuredvalue of T_(M). In the preferred embodiment of this approach, theadjustment to the value of Tc at the position of the measured T_(M) toobtain a limiting Tc may be determined by those skilled in the art froma continuously measured or predicted axial power distribution (AO) forthe instrumented locations. A similar approach is used to adjust thevalue of the measured T_(M) values to calculate the value of the peakT_(M) as a function of time. This can be accomplished by those skilledin the art resulting in an expression for adjusted peak clad temperatureof the form:

T _(M) ^(A)(t)=(1+β(t))T _(M)(t)

T _(C) ^(A)(t)=(1+θ(t))T _(C)(t)  Eq. 4

Once the distributions of T_(M) ^(A)(t) and T_(C) ^(A)(t) values at agiven time are determined from measured or expected reactor powerdistribution information in the fuel rods expected to have the highestrelative power located in the fuel assemblies expected to have thehighest relative power, the limiting values of T_(M)(t) and T_(C)^(A)(t) can be determined. A turbine runback and/or reactor trip can beestablished at a properly conservative setpoint for each parameter.

The foregoing methodology enables the reactor protection system todetermine whether to trip the reactor using data more directly alignedwith the key parameters of importance in determining whether the fuelrods will experience a Departure from Nucleate Boiling (DNB) or fuelpellet melting. This methodology eliminates the need for complex nuclearpower distribution measurement codes and DNB prediction and analysismethods. Furthermore, the foregoing methodology may be used in bothexisting and future pressurized water reactor, boiling water reactor andlight water reactor types. Additionally, the sensors needed for thistechnique may be integrated into the fuel assemblies.

FIG. 4 is a flowchart of a method of determining T_(M) and Tc in anoperating nuclear core in accordance with an example embodiment of thedisclosed concept. The method begins at 100 with directly measuring thetemperatures at one or more locations on a fuel within the one or morefuel rods of a nuclear reactor. Any suitable sensing system and sensors,such as those described in connection with FIGS. 1-3, may be employed todirectly measure the temperature. The method then moves to 102 withidentifying a hottest temperature of the fuel and a core location wherethe hottest temperature is measured. The hottest temperature may beidentified based on the outputs of sensors, such as sensor 20, locatedat various axial positions in fuel rods. The sensor measuring thehottest temperature may be identified, for example, by identificationinformation output by the sensor, and the sensor's location within thecore may be identified, for example, by referencing the information onthe installation location of the sensor. Next, at 104, the maximumtemperature of the coolant exiting the core at the core locationcorresponding to the hottest temperature and the minimum flow rate ofthe coolant are measured. These values may be measured using suitablesensors already existing in nuclear reactors. The method proceeds to 106with determining Tc from the hottest measured temperature of the fuel,the maximum temperature of the coolant exiting the core at the corelocation and the minimum flow rate of the coolant. For example,Equations 1-3 may be employed to determine Tc. Knowledge of the heattransfer characteristics of the fuel pellet and fuel rod structuralmaterials may also be employed.

The method of FIG. 4 may be implemented in a sensor system such as thesensor system of FIG. 1. For example, step 100 may be implemented withone or more sensors 20. Steps 102-106 may be implemented in a processor,such as signal processing elements 44. The method of FIG. 4 may alsoinclude additional steps, such as determining whether T_(M) and/or Tcexceed threshold levels and, if so, implementing protective measuressuch as a turbine runback and/or reactor trip, which can be implementedin an RPS.

The systems and method described herein provide improved measurement andcalculation of T_(M) and Tc, while prior systems and methods made moreconservative assumptions that limit the operating power levels and powerdistributions allowed in reactor designs. The systems and methodsaccording to the disclosed concept allow fuel rods to operate muchcloser to the actual safety limits for fuel pellets and claddingoperation, which can improve energy generate for the same amount of fuelby 28%.

While specific embodiments of the invention have been described indetail, it will be appreciated by those skilled in the art that variousmodifications and alternatives to those details could be developed inlight of the overall teachings of the disclosure. Accordingly, theparticular embodiments disclosed are meant to be illustrative only andnot limiting as to the scope of the invention which is to be given thefull breadth of the appended claims and any and all equivalents thereof

What is claimed is:
 1. A method of determining a maximum measuredinternal fuel rod temperature and a peak clad temperature of one or moreof fuel rods in an operating nuclear core comprising the steps of:directly measuring the temperatures at one or more locations within theone or more of the fuel rods; identifying a hottest temperature withinthe one or more fuel rods as the maximum measured internal fuel rodtemperature and a core location where the hottest temperature ismeasured; measuring the maximum temperature of coolant exiting the coreat the core location where the hottest temperature is measured and theminimum flow rate of the coolant; and determining the peak cladtemperature from the maximum measured internal fuel rod temperature, themaximum temperature of the coolant exiting the core at the core locationwhere the hottest temperature is measured and the minimum flow rate ofthe coolant.
 2. The method of claim 1 wherein the directly measuringstep measures the temperature along a plurality of axial locations inthe one or more fuel rods.
 3. The method of claim 2 wherein in theplurality of axial locations include the tops and bottoms of the one ormore fuel rods.
 4. The method of claim 1 further comprising: determiningthe bulk coolant temperature from the maximum temperature of the coolantexiting the core at the core location where the hottest temperature ismeasured and the minimum flow rate of the coolant.
 5. The method ofclaim 4, wherein determining the peak clad temperature is based onknowledge of heat transfer and geometric characteristics of fuel pelletsin the one or more fuel rods and cladding of the one or more fuel rods.6. The method of claim 5, wherein determining the peak clad temperatureincludes determining the peak clad temperature using the followingequation:${T_{C}(t)} = {{T_{F}(t)} + \frac{{T_{M}(t)} - {T_{F}(t)}}{\phi (t)}}$Where:${\phi (t)} = \left( {{\frac{rh}{2{k_{f}\left( {T_{F}(t)} \right)}}\frac{A_{r + c}}{A_{r}}} + {\frac{ch}{k_{c}}\frac{A_{r + c}}{A_{m}}} + 1} \right)$And:$A_{m} = \frac{2\pi \; {cL}}{\ln \left\lbrack \frac{r + c}{r} \right\rbrack}$Where: r = fuel  pellet  diameter c = cladding  thicknessL = fuel  rod  length kf = fuel  pellet  thermal  conductivitykc = cladding  thermal  conductivityAr = cross  section  area  of  fuel  pelletAr + c = cross  sectional  area  of  fuel  pellet  and  claddingh = cladding  heat  transfer  coefficient  by  convection. 7.The method of claim 1 wherein the step of directly measuring thetemperature at one or more locations on the fuel is performedsubstantially continuously.
 8. The method of claim 1, furthercomprising: comparing the peak clad temperature and/or the maximummeasured internal fuel rod temperature with one or more thresholdvalues; and implementing protective measures in response to determiningthat the peak clad temperature and/or the maximum measured internal fuelrod temperature with one or more threshold values.
 9. The method ofclaim 8, wherein the protective measured include a turbine runback or areactor trip.
 10. A system to determine a maximum measured internal fuelrod temperature and a peak clad temperature of one or more of fuel rodsin an operating nuclear core, the system comprising: sensors disposed inone or more of the fuel rods and being structured to directly measurethe temperatures at one or more locations within the one or more of thefuel rods; an instrument thimble disposed outside the one or more fuelrods and being structured to receive the measured temperatures from thesensors; signal processing elements structured to receive the measuredtemperatures from the sensors and to: identify a hottest temperaturewithin the one or more fuel rods as the maximum measured internal fuelrod temperature and a core location where the hottest temperature ismeasured, receive a measured maximum temperature of coolant exiting thecore at the core location where the hottest temperature is measured andthe minimum flow rate of the coolant, and determine the peak cladtemperature from the maximum measured internal fuel rod temperature, themaximum temperature of the coolant exiting the core at the core locationwhere the hottest temperature is measured and the minimum flow rate ofthe coolant.
 11. The system of claim 10, wherein the sensors arepassive.
 12. The system of claim 10, wherein the instrument thimble isstructured to interrogate the sensors.
 13. The system of claim 10,wherein at least one of the sensors includes a resonant circuitstructured to change its resonant frequency based on the directlymeasured temperature.
 14. The system of claim 10, wherein at least oneof the sensors includes a liquid metal thermometer, a ferritic core, andan inductor coil, wherein the liquid metal thermometer is structured tocause the ferritic core to move into or out of the inductor coil basedon changes in temperature.